A family of Artin-Schreier curves with many automorphisms

Algebraic geometry codes are obtained from certain types of curves over finite fields. Since the length of such a code is determined by the number of rational points on the curve, it is desirable to use curves with as many rational points as possible. We investigate a certain class of Artin-Schreier curves with an unusually large number of automorphisms. Their automorphism group contains a large extraspecial subgroup. Precise knowledge of this subgroup makes it possible to compute the zeta functions of these curves. As a consequence, we obtain new examples of curves that attain the provably maximal (or minimal) number of points over an appropriate field of definition.